The NWS earlier noted reports of five deaths in the area, but only one fatality in Houston has been confirmed.

Two deaths have so far been confirmed from the storm since it made landfall:

In Aransas County, where Rockport is the chief town, a person died in a house fire on Friday night

A woman died in Houston as she drove through flooded streets on Saturday

Houston Mayor Sylvester Turner has urged residents not to call emergency services unless their situation is life-threatening and they need to be rescued.

"Don't get on the road. Don't assume this storm is over," he said.

Officials in Harris County, of which Houston is the county seat, have asked people who own boats to help with rescues.

Houston Bush Airport has announced that all commercial flight operations have been stopped until further notice. Houston's other airport, Hobby, is also shut, with runways completely flooded.

In Washington, the White House said that President Trump would visit Texas on Tuesday to survey storm damage. Mr Trump had earlier said that he would go as soon as it was possible to do so "without causing disruption".

Image copyrightREUTERSImage captionMore than 3,000 National Guard members are on-hand to help in Houston and elsewhere

At 14:00 local time (19:00 GMT) on Sunday, the NWS said Houston had had an August rainfall total of 25.50in (64.8cm), making it the wettest month on record.

Roads have turned into rivers

by James Cook, BBC News, Houston

Inside Houston a disaster is unfolding. The motorways are deserted except for fire engines, police cars and other emergency vehicles.

Moving around the city is extremely difficult and dangerous. And yet some people are still driving, adding to the pressure on city authorities

Everywhere you look cars are being abandoned as people scramble to find high ground. Roads have turned to rivers along which evacuees are being taken to safety in boats and in army-style, open-back lorries.

Image copyrightTWITTER/@CAROLEENAM/REUTERS

They are huddled together under blankets and towels, glad to be alive. And still the rain comes teeming down, bouncing off the ground and bursting out of drains.

Flooding in the Houston area is expected to worsen and "could become historic", with "potentially significant flooding also expected in other saturated areas of south-east [Texas]", the forecaster says.

Like Houston, the island city of Galveston was also hit by "epic catastrophic flooding" overnight, the NWS added.